Decoding entanglement in soft materials

• Applicant: Professorin Dr. Myfanwy E. Evans
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 468308535

Entanglement, a concept encompassing knots, links and more generic tangling of 1- dimensional strands, is a fundamental phenomenon in the interplay of geometric structure and macroscopic functionality of various complex and hierarchical materials. While a general consensus has been reached that entanglement is an important structural feature of soft materials, the quantification and role of entanglement is yet to be solved. I propose to convert recent cross-disciplinary theoretical advances in the geometric construction of tangling into a precise description and basic functioning of material microstructures that in- volve entanglement.The idea of entanglement pervades many disciplines in the sciences, from the folding of proteins, through polymeric materials, to knotted molecules in molecular machines. The challenge of such a broad concept is to extract system independent descriptions and behaviour, ascertaining what is truly the function of entanglement. Given the recent explosion of synthesis techniques in knotted molecules and DNA origami, the development of a theoretical basis is timely. More specifically, we encounter two main open questions: How can tangled material microstructures be accurately described? What is the relation- ship between microstructure tangling and macroscopic activity?I will address these fundamental questions, whose core lies in soft matter physics, from the perspective of applied geometry and topology. This will provide a further step towards the elusive target of the geometric structure-function relationship for entangled materials. In doing so, I will bridge the divide between geometric techniques and the natural sciences by developing theory at the disciplinary interface. The introduction of robust geometric tools into the biophysical sciences will facilitate the analysis of complex systems at a deeper level, changing the research landscape by providing a link between the microscopic and macroscopic scales.

• DFG Programme: Research Grants